Sunday, March 6, 2016

Please stop writing dilution ratios as though they were fractions

Many biologists seem to not know how to write dilution notation properly. The colon ":" and the slash "/", both have distinct and well defined meanings. People (biologists, at least) usually use the slash properly, but in many situations use the colon as if it were a slash. Please, if you mean slash, write slash. If you mean colon, write colon. Do not write colon when you actually mean slash.

Let me explain the difference:

Roughly speaking, a colon separates parts of the mixture of equal standing. A slash separates a part from the whole. In math-speak: a colon indicates a ratio, and a slash indicates a fraction.

To convert from colon notation to slash notation, the general formula is:
x:y is equivalent to x/(x+y)
where x and y are individual components of a mixture.

For example:
1:1 means 1 part x to 1 part y, such that y does not include x.
If I write in a protocol make a dilution of "1:1 ethanol into water" I mean "combine equal parts ethanol and water", for example "10 mL ethanol with 10 mL water". If I want to be really precise, I'll even include the units (or dimensions) for each. For example "make a mixture of 1:1 (volume:volume) ethanol:water", or "make a mixture of 1:1 (grams:milliliters) ethanol:water". Writing in this way is precise, and tells the reader exactly how to create the solution in question.

Slash notation is different, and is sometimes more ambiguous.
1/2 means 1 part x in 2 parts total
In slash notation the number on the left is some part of the mixture, and the number on the right is the whole mixture. Thus, the slash notation equivalent of 1:1 is 1/2.
Biologists sometimes ignore the fact that the volume of mixing liquids isn't additive. The non-additivity of mixtures means that volume/volume fractions are not very good ways to describe solutions. Molarity, and mass/volume are much better.

Colon (ratio) notation is usually more appropriate to use in describing mixtures and solutions in biology than slash (fraction) notation. I think what trips people up, is that when the second number is really big, it doesn't look quite right for it to not be a nice round number:
The correct form:
1:199
is not as aesthetically pleasing as the incorrect form:
1:200

There is also a temporal distinction between the two notations, particularly when speaking of volumes. x:y (volume:volume) implies that x and y are volumes before mixing. In fraction form x/z, z indicates the volume of the mixture, so it has to be a measurement after the mixing has occurred. Whether x is a volume before or after mixing is ambiguous.

Conclusion:
Be aware of the distinct mathematical meanings of colon (:) and slash (/). Do not use colon when you mean slash. Don't be alarmed when the numbers in your ratio aren't nice round numbers, do not round them to the nearest 10 for neatness.

When slash notation, if there is a volume as the numerator, consider converting the volume to mass or moles. If you must leave it as a volume, consider using colon notation instead.